Gel filtration is run in native condition so one peak doesn't mean automatically one object as apparent MW isn't specific enough (one MW is shared by different proteins). The object you actually purified might be formed from the assembly of different polypeptides which might be separated by SDS PAGE if these polypeptides exhibit different MW. An other possibility is that your native object is a single polypeptide but it has been cut into several polypeptides without affecting its overall structure. So what you see by SDS PAGE might be the separation of the different polypeptide generated by the cleavage of the original protein.
1) Impurities are coeluting with main protein fraction. In this case, you can use column with smaller pore size particles. Sometimes, reducing the sample volume or flow rate or increasing column length may also help when the difference between molecular size of impurity and your protein is very large. (this is the majorly the case when doing preparative SEC)
2) your protein is degrading in the buffer solution on storage. In which case you will get smear of bands. You might also be forming covalent dimers but these things are less likely to happen.
3) Non-specific binding of impurity to the column may also give broad peak which eventually merges with your main protein peak. This may be avoided by using high salt concentration in mobile phase.
There may be other proteins present, but due to low sensitivity of UV detector (lamp life and dirty UV filter) not showing peak and only group separation is detected.